The wireless channel in a wireless communication system constitutes a hostile propagation medium. This medium suffers from fading, which is caused by the destructive addition of multiple replicas of a transmitted signal which are detected by a receiver from multiple paths. Another problem with wireless data transmission is interference from other users. One approach to combating fading and interference is to provide a receiver with several identical replicas of a transmitted signal. This is accomplished by diversity techniques. One such technique is antenna diversity, in which an array of antennas is deployed at the transmit side and/or the receive side of a wireless link. Another name for a system which employs antenna diversity at both the transmit side and receive side of a wireless link is a multiple-input multiple-output (MIMO) system.
FIG. 1 depicts a typical MIMO system, generally indicated at 10, which is known in the prior art. Digital data 12 is encoded by an encoder 14 using one of several encoding techniques, such as quadrature amplitude modulation (QAM). The encoded data is demultiplexed into several data streams by a demultiplexer 16. The demultiplexer 16 feeds the multiple data streams to a plurality of modulators 18a-18Nt using orthogonal frequency division multiplexing (OFDM) to be discussed hereinbelow. The modulated signals are then transmitted through the wireless medium simultaneously via Nt antennas 20a-20Nt. While traveling through the wireless medium, some of the signals transmitted from the antennas 20a-20Nt may reflect from obstructions 22, 24, such as buildings, cars, trees, and the like. Signals transmitted directly from all of the sending antennas 20a-20Nt and indirectly from the obstructions 22, 24 are received at Nr receive antennas 26a-26Nr. A MIMO receiver 28 demodulates, multiplexes, and decodes the several received data streams into a single received data stream. Designating the signal received at each of the receive antennas 26a-26Nr as yj, and the signals transmitted at the sending antennas 20a-20Nt as xi, the signals received at each of the receive antennas 26a-26Nr can be represented as a set of linear equations wherein “h” is the signal weight, as follows:y1=h11x1+h12x2+ . . . +h1NtxNt y2=h21x1+h21x2+ . . . +h2NtxNt yNr=hNr1x1+hNr2x2+ . . . +hNtNrxNt 
As can be seen from the above equations, in making their way from the sending antennas 20a-20Nt to the receive antennas 26a-26Nr, the independent signals, x1 through xNt, are all combined. Traditionally, this “combination” has been treated as interference. By treating the channel as a matrix, however, the independent transmitted streams, xi, can be recovered by estimating the individual channel weights hij. The transmitted signals xi and the received signals yj can be collected into vectors, x and y of dimensions Nt×1 and Nr×1, respectively, and the channel weights hij can be collected into a channel matrix H of dimensions Nr×Nt. The channel input-output relationship in matrix-vector form can be expressed as:y=Hx+v where v is a vector of channel noise to be discussed hereinbelow. Having estimated H, one can solve for the values of the transmit vector x by multiplying the receive vector y by the inverse of H and subtracting v therefrom.
Because multiple data streams are transmitted in parallel from different antennas, there is a linear increase in throughput with every pair of antennas added to the system. In current wireless communication schemes, there is not only a need to increase throughput, but also a need to improve the quality of the received signals. Because of reflections from different obstructions 22, 24, sometimes the reflected signals add up in phase and sometimes they add up out of phase causing a “fade”. A fade causes the received signal strength to fluctuate constantly. Different sub-channels (the transmitted signals) are distorted differently, which leads to a sub-channel becoming frequency selective. As throughput (data rate) increases, frequency selectivity also increases. Systems employing orthogonal frequency division multiplex (OFDM) modulation convert frequency selective channels into a set of parallel flat-fading sub-channels, thus enabling low complexity equalization. The “orthogonal” part of the name refers to a property of sub-channels in which the frequencies in each sub-band are integer multiples of a fundamental frequency. This ensures that even though the sub-channels overlap, they do not interfere with each other, thereby removing the frequency selectivity and thus increasing spectral efficiency. The wedding of MIMO and OFDM for high speed applications combines high throughput with high spectral efficiency.
The operations performed on a transmit side of a datastream of a block of symbols of length N as it passes through an OFDM modulator include the steps of: encoding the block of symbols using an encoding scheme such as quadrature amplitude modulation (QAM); passing the encoded symbols through a serial-to-parallel converter; performing an Inverse Fast Fourier Transformation (IFFT) on the parallel data; prepending to the parallel data a cyclic prefix (CP) of length LCP≧L containing a copy of the last LCP samples of the parallel-to-serial converted output of the N-point IFFT; and passing the data through the parallel-to-serial converter. The length of the cyclic prefix (CP) being greater than or equal to the length of the discrete-time baseband channel impulse response (i.e., LCP>L) guarantees that the frequency-selective MIMO fading channel decouples into a set of parallel frequency-flat MIMO fading channels. The symbols are converted back to analog form and transmitted from transmit antennas into the wireless medium.
On the receive side of the wireless medium, an antenna receives an OFDM-modulated signal and passes the signal through an OFDM de-modulator. The OFDM de-modulator performs the following operations: stripping the cyclic prefix; converting the serial data to parallel form; performing an N-point Fast Fourier Transformation (FFT) on the data, converting the parallel data back to serial form, and decoding the data (e.g., via a QAM-decoder).
To improve data transmission and error performance still further, finite-rate transmit beamforming is applied to multiple data symbols x to be transmitted for each of p sub-carriers. In finite-rate transmit beamforming, some of the data bits received at the receiver 28 are fed back to the transmitter/modulators 18a-18Nt so that the transmitter can adapt to changing channel conditions via beamforming weights applied to the signal to be transmitted. In a multi-antenna wireless communication system having Nt transmit-antennas and Nr receive-antennas, each transmit antenna employing OFDM using Nc subcarriers, the fading channel between the μ-th transmit-antenna and the υ-th receive-antenna is assumed to be frequency-selective but time-flat, and is described by a linear filter with LL+1 taps, as follows:hυμ(n):={hυμ(n;0), . . . , hυμ(n;LL)},where n is the OFDM symbol index and LL is the channel order. The channel impulse response includes the effects of transmit-receive filters, physical multipath, and relative delays among antennas. With p denoting the OFDM subcarrier index, the frequency response between the μ-th transmit-antenna and the υ-th receive-antenna on the p-th subcarrier is:
                    H        υμ            ⁡              [                  n          ;          p                ]              =                  ∑                  l          =          0                LL            ⁢                          ⁢                                    h                          υ              ⁢                                                          ⁢              μ                                ⁡                      (                          n              ;              l                        )                          ⁢                  ⅇ                      -                          j                              2                ⁢                π                ⁢                                                                  ⁢                                  pl                  /                                      N                                          c                      ,                                                                                                                ,      p    =    0    ,  …  ⁢          ,            N      c        -    1.  At the p-th subcarrier of the n-th OFDM symbol, by collecting the transmitted symbols across Nt transmit antennas in an Nt×1 vector x[n;p], and the received symbols across Nr receive-antennas in an Nr×1 vector y[n;p], the channel input-output relationship on the p-th subcarrier is:Y[n;p]=H[n;p]x[n;p]+v[n;p], where v[n;p] is additive white Gaussian noise (AWGN) with each entry having a variance with each entry having variance N0 and H[n;p] is the Nr×Np channel matrix with the (υ,μ)-th entry being Hυμ(n;p).
With finite rate transmit beamforming, an information symbol s[n;p] is multiplied by an Nt×1 beamforming vector w[p] to form x[n;p]=w[p]s[n;p], which is then transmitted through the p-th sub-carrier of the OFDM system. The input-output relationship on the p-th sub-carrier can be expressed as:y[n;p]=H[p]w[p]s[n;p]+v[n;p]Based on feedback, the transmitter seeks to match the beamforming vector w[p] to the channel H[p] to improve system performance.
If the transmitter has perfect knowledge of H[p], the optimal beamforming vector will be the eigenvector of HH[p] H[p], where HH[p] is the Hermitian transpose of H[p], corresponding to the largest eigenvalue to maximize the signal to noise ratio (SNR) on each sub-channel, where the SNR is designated as γ[p], and:
      γ    ⁡          [      p      ]        =                    E        S                    N        0              ⁢                                                H            ⁡                          [              p              ]                                ⁢                      w            ⁡                          [              p              ]                                                  2      where Es is the average energy per symbol s[n;p] and ∥*∥ denotes a two-norm of a vector or a matrix. Assuming a maximum ratio combining (MRC) receiver, the received symbols ŝ[n;p] are:ŝ[n;p]=wH[p]HH[p]y[n;p]where wH[p] is the Hermitian transpose of w[p] and HH[p] is the Hermitian transpose of H[p].
Finite rate transmit beamforming satisfies the condition that channel behavior is known to both the receiver and transmitter. This behavior is represented by the matrix H[p], which can be estimated by the receiver, which has knowledge of the effects of the wireless channel. This means that the receiver would have to estimate H[p] for each OFDM frequency channel, and send all of this information back to the transmitter. This information is ancillary data that is not part of the information transmitted. Thus, it is desirable that the amount of bandwidth dedicated to feedback information be kept to a minimum. In fact, the transmission of a matrix is an expensive operation, since a matrix has many elements (the square of the dimension).
A technique known as finite rate feedback can be employed to minimize the data to be transmitted from the receiver to the transmitter, yet maximize the knowledge gained by the transmitter about the channel to improve beamforming. One version of finite rate feedback is “per subcarrier feedback.” In per subcarrier feedback, feedback is done separately on all subchannels. Assuming that B1 feedback bits are available per subcarrier, the transceiver will need a codebook CB of size 2B1, which is a collection of beamforming vectors {w1, . . . , w2B1}. It is assumed that the codebook CB is the same across subcarriers. The beamforming vector is chosen at the receiver to maximize γ[p] at the p-th subcarrier to be:
            w      opt        ⁡          [      p      ]        =      arg    ⁢                  ⁢                  max                  w          =          W                    ⁢                                                                              H                ⁡                                  [                  p                  ]                                            ⁢              w                                            2                .            The index of wopt[p] will be fed to the transmitter B1 feedback bits. The transmitter then switches to wopt[p] after finding wopt[p] via the index in its own codebook. Unfortunately, with finite rate feedback, NcB1 bits need to be fed back to the transmitter, which is a large number of bits considering that Nc is usually large.
Another technique known in the art is the one employed by Choi and Heath known as interpolation, which is described in the “Interpolation Based Transmit Beamforming for MIMO-OFDM with Limited Feedback,” in Proc. Of Int. Conf. on Communications, Paris, France, June 2004, vol. 1, pp. 249-253, which is incorporated herein by reference. In the interpolation technique, Nc subcarriers are split into Ng groups with Nc/Ng consecutive subcarriers per group. Only {wopt[lNg]}
      {                  w        opt            ⁡              [                  lN          g                ]              }        l    =    0              N      e        /          N      g              -        1            bits will be fed back to the transmitter, and the rest of the subcarriers rely on the following interpolation:
      w    ⁡          [                        lN          g                +        k            ]        =    ⁢                                                                        (                                  1                  -                                      k                    /                                          N                      g                                                                      )                            ⁢                                                w                  opt                                ⁡                                  [                                      lN                    g                                    ]                                                      +                                                                                          ⅇ                                  jθ                  l                                            ⁡                              (                                  k                  /                                      N                    g                                                  )                                      ⁢                                          w                opt                            ⁡                              [                                                      (                                          l                      +                      1                                        )                                    ⁢                                      N                    g                                                  ]                                                                                                                                                          (                                      1                    -                                          k                      /                                              N                        g                                                                              )                                ⁢                                                      w                    opt                                    ⁡                                      [                                          lN                      g                                        ]                                                              +                                                                                                                        ⅇ                                      jθ                    l                                                  ⁡                                  (                                      k                    /                                          N                      g                                                        )                                            ⁢                                                w                  opt                                ⁡                                  [                                                            (                                              l                        +                        1                                            )                                        ⁢                                          N                      g                                                        ]                                                                                    where θ1 is chosen from a finite set {ejn2π/P}n=0P-1. The feedback required for the interpolation method is (Nc/Ng)(B1+log2P) bits, which is a significant improvement over the finite rate feedback technique. Unfortunately, the interpolation technique suffers from “diversity loss,” in which bit error rate (BER) levels off as the signal-to-noise ratio (SNR) increases.
Thus, despite efforts to date, a need remains for methods that are effective in reducing feedback in an adaptive MIMO-OFDM system while maintaining performance. These and other needs are satisfied by the methods/techniques described herein.